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Problem 2-For a rectangular metallic waveguide of width b-2 cm and height a-3 cm, calculate the following. (a) What are the supported mode(s) at 6 GHz? Calculate phase velocity and (b) What are the supported mode(s) at 8 GHz? Calculate phase velocity and (c) Plot the group velocity dispersion parameter β2 (-d+p) for the lowest order (d) Consider the lowest order mode supported in the rectangular waveguid<e group velocity of those mode(s) at 6GHz. group velocity of those mode(s) at 8 GHz. mode as a function of o. Provide the dispersion coefficient D at 6 GHz. where the following modulated signal propagates: cos a (t pl where %,-group velocity ator and vpl.-phase velocity ato. The modulated signal has a center frequency at 6 GHz (01-2*T*f;; 6 GHz) with the modulation frequency 0.2 GHz (&0-2*T*A: 에.=0.2 GHz) and modulation index m-0.3. What are the group velocities of the lowest order mode in the waveguide at 5.8 GHz and 6.2 GHz?
Plot the waves (E field vs z) similarly to the Slide #25 of Lecture Notes 2 for this modulated signal at to-0 sec, A-1 ns (show at least three frames). t- Group velocity (e) Repeat (d) for the modulated signal with a center frequency at 6.5 GHz (o 2-2*πh; f2-6.5 GHz) with the modulation frequency 0.2 GHz (&o-2*π*A: T-0.2 GHz) and modulation index 0.3. What are the group velocities of the lowest order mode in the waveguide at 6.7 GHz and 6.3 GHz? Plot the waves (E field vs z) similarly to the Slide #25 of Lecture Notes 2 for this modulated signal at to-0 sec, Δ 1 ns (show at least three frames). where vg.-group velocity at ω2 and v,,-phase velocity at ω2. (f) Repeat (d) for the modulated signal with a center frequency at 5.5 GHz (c03-2* 6:6-5.5 GHz) with the modulation frequency 0.2 GHz (0-2* *A: dT-0.2 GHz) and modulation index -0.3 What are the group velocities of the lowest order mode in the waveguide at 5.7 GHz and 5.3 GHz? Plot the waves (E field vs z) similarly to the Slide #25 of Lecture Notes 2 for this modulated signal at to 0 sec. Δ 1 ns (show at least three frames). where v-group velocity at o and v, phase velocity at o.
(g) Compare the plots of (d), (e), and (f) and provide the group delay differences seen for (e) and (f) in reference to (d). After 1 meter propagation, how much group delay difference do you observe between (e) and (f)? Does this correspond to the value predicted from the dispersion coefficient calculated in (c)? (h) Using the superposition principle, repeat the plot of the composite (sum) of the three E fields ( E (z)+E, (z.t)+E, (z.t). After 1 meter propagation, how much does the signal spread in time?
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